Ptolemaic Model

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Ptolemaic Model
Ptolemaic Model
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100AD Alexandria, Egypt – the Almagest
Geocentric, uniform circular motion
Planets carried around Earth on Crystalline Spheres
Predicted Moon & Sun positions okay
A few problems
Problem: Hipparchus 150BC
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21 March to 21 Sept not equal to 21 Sept to 21 March
10+30Apr+31May+30Jun+31July+31Aug+21Sep=184 days
9+31Oct+30Nov+31Dec+31Jan+28Feb+21Mar=181 days
Sun/Earth moves too fast for half its orbit. Not uniform circular motio
Earth placed off center of circle – Not Geocentric
Planet/Sun has uniform circular motion as seen from Equant point
Inferior and Superior Planets
•  Inferior –closer to Earth than Sun & tied to Earth-Sun line
•  Superior –farther from Earth than the Sun
Problem: Planets Wander thru Stars
•  Prograde=Direct Eastward motion of planets with respect to stars
•  Retrograde=Backward Westward motion of Planets relative to stars
•  Retrograde motion happens when planet is brightest & opposite sun
Ptolemy’s Explanation of
Retrograde Motion
•  Deferent is the big circle
•  Epicycle is small circle
•  Preserves uniform circular
motion
•  Planet closest to Earth and
thus brightest during
retrograde
Retrograde Animation
•  Planet travels on epicycle
•  Epicycle travels on deferent
Ptolemy’s Planet Spacing
•  Solar System had to be
big enough to keep
planets from colliding
•  Venus and Mercury
were tied to sunline
•  Needed 80 circles
Copernicus 1473-1543
•  Time of first printing press (~1450)
•  Columbus discovers America showing
Ptolemy’s map incomplete
•  Martin Luther&Reformation 1483-1546
•  Church administrator in Poland
•  Wrote pamphlet on heliocentric system
•  On death bed published the book
“nobody read” 1542
Copernican
Revolution
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Sun centered = Heliocentric
Earth is –NOT- special
Paradigm shift (Kuhn 1962)
Much simpler scientific theory
But he retained uniform
circular motion & epicycles
•  Planetary tables were not a
great improvement
Retrograde According to Copernicus
Retrograde Motion in the
Copernican System
Planetary
Configurations
•  Inferior and superior planets
•  Oppositions, conjunctions,
elongations, and quadratures
•  Relative planet spacing from
the geometry
•  Sine (Greatest Elongation) =
Orbital radius / Earth’s orbital
radius
Retrograde motion is:
a.  The apparent backward=westward motion of a
planet relative to stars as seen from Earth
b.  Occurring at opposition to sun when the planet
is at its brightest
c.  Explained by the Greeks by a system of
Deferents and Epicycles
d.  Explained by Copernicus by the Earth lapping
the superior planets
e.  All of these

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